The basswood would certainly lighten up the bass as far as weight. Depending on the finish, that combo may be more to give the appearance of an all mahogany bass but not necessarily feel like one. It is a popular tonewood for guitars by many progressive builders, but it's fragile, soft nature leaves me from recognizing any tonal advantage.
Not to dogpile on the discouragement of it's use, consider this. The Fender Precision Bass, Jazz Bass, and EBMM Stingray all have a similar platform. They have either an alder or ash body and are paired with either a maple/maple or maple/rosewood neck, and they are all distinctly different sounding basses despite their similarities. The differences are attributed to the pickups and electronics.